Changing moment of inertia in rigid body simulation
The moment of inertia of rigid bodies in Blender is currently determined only by their collision shape. In principle this could be defined separately from any collision geometry, but for most artistic purposes this approach is easier i suppose.

More importantly even, changes to the shape/inertia will not have any effect on the motion state of bodies, since the motion state is only defined by position/orientation and velocity and does not describe energetic state directly. After all it is called a Rigid Body simulation, which implies that the shape of bodies does not change over time.

This being said, you may have already given the answer: approximate changing moment of inertia by using connected rigid bodies. I've made a test using a symmetric set of secondary bodies (like the arms of the ice skater), which are connected to the central body with slider constraints. Unfortunately it looks like animating the constraint settings (x axis limits) does not work either, but perhaps there is still a solution.